Based on Sydney's study, which of the following statements is true?

Linear functions and exponential functions are different, with distinct properties.

Linear functions and exponential functions are basically the same.

Exponential functions are a type of linear functions.

Linear functions are a type of exponential functions.

Could an explicit formula for the nth rectangular number be considered a function?

Yes, because it assigns a unique output for each input.

No, because it does not assign a unique output for each input.

Yes, because it can have more than one output for each input.

No, because rectangular numbers do not have a formula.

If an explicit formula for the nth rectangular number is considered a function, what would be the domain and range of the function?

Domain: positive integers, Range: rectangular numbers

Domain: all real numbers, Range: all real numbers

Domain: rectangular numbers, Range: positive integers

Domain: all integers, Range: all integers

If each of the 20 students in a school musical is assigned exactly one role and each role is played by only one student, would this be an example of a function?

Yes, because each student (input) is assigned a unique role (output).

No, because a student can play more than one role.

Yes, because multiple students can play the same role.

No, because roles are not a numerical output.

If the instrumental parts are the domain and the musicians are the range, and no two musicians have the same instrumental part, is the assignment of instrumental parts to musicians a function?

Yes, because each part (input) is assigned to exactly one musician (output).

No, because one musician can have two different parts.

Yes, because multiple musicians can have the same part.

No, because there are more parts than musicians.

What would be the meaning of A(Piano) = Scott in the context of the orchestra?

Scott is assigned to play the piano.

The piano is assigned to play Scott.

Scott is assigned to two instrumental parts.

The piano is not part of the orchestra.

If there are 10 instrumental parts but 13 musicians in the orchestra, and some instrumental parts will have two musicians assigned so that all musicians have parts, is the assignment of instrumental parts to musicians a function?

No, because some parts are assigned to more than one musician.

Yes, because each musician is assigned to at least one part.

Yes, because the musicians can alternate parts.

No, because the musicians are more than the instrumental parts.

What would be the meaning of A(piano) = Scott if the assignment of instrumental parts to musicians is considered a function?

Scott is assigned to play the piano part.

The piano part is assigned to play Scott.

Scott is one of the possible musicians who could play the piano part.

The piano part is one of the instruments Scott could play.

What is the exponential decay model chosen by scientists to model the declining population of a remote island since the year 1950?

P(x) = 2350(0.95)^x, where x is the number of years since 1950.

P(x) = 1950(0.95)^x, where x is the number of years since 2350.

P(x) = 2350(0.05)^x, where x is the number of years since 1950.

P(x) = 2350(1.05)^x, where x is the number of years since 1950.

What is the y-intercept of the graph?

The point where the graph crosses the y-axis

The point where the graph crosses the x-axis

Over what intervals is the function increasing?

When the graph moves upwards from left to right

When the graph moves downwards from left to right

When the graph is a straight horizontal line

When the graph makes a parabolic curve

Over what intervals is the function decreasing?

When the graph moves downwards from left to right

When the graph moves upwards from left to right

When the graph is a straight horizontal line

When the graph makes a parabolic curve

According to the Mid-Module Assessment Task, what is expected from a student to achieve a STEP 1 level of mastery for assessment task items 1-a to 1-d?

Student is unable to identify the sequence as arithmetic and unable to create an explicit formula for finding the number of students who can be seated at n tables.

Student provides correct entries for the table and explains that the sequence is arithmetic because each successive term is two more than the last term.

Student recognizes the sequence as arithmetic but displays a logic error in the explicit formula for the sequence.

Student writes an explicit formula for the sequence using an appropriate sequence notation, such as f(n) or a_n, and correctly relates the constants of the formula to the context of the problem.

What does STEP 2 indicate about a student's understanding for assessment task items 1-a to 1-d?

Student recognizes the sequence as arithmetic but displays a logic error in the explicit formula for the sequence.

Student provides correct entries for the table and explains that the sequence is arithmetic because each successive term is two more than the last term.

Student is unable to identify the sequence as arithmetic and unable to create an explicit formula for finding the number of students who can be seated at n tables.

Student writes an explicit formula for the sequence using an appropriate sequence notation, such as f(n) or a_n, and correctly relates the constants of the formula to the context of the problem.

What is required for a student to achieve STEP 4 level of mastery for assessment task items 1-a to 1-d?

Student writes an explicit formula for the sequence using an appropriate sequence notation, such as f(n) or a_n, and correctly relates the constants of the formula to the context of the problem.

Student provides correct entries for the table and explains that the sequence is arithmetic because each successive term is two more than the last term.

Student is unable to identify the sequence as arithmetic and unable to create an explicit formula for finding the number of students who can be seated at n tables.

Student recognizes the sequence as arithmetic but displays a logic error in the explicit formula for the sequence.

According to the rubric, what is the expectation for a student to demonstrate at level 4 for standard F-IF.A.2?

Student articulates that 10 rows of 9 tables are needed to seat 189 students and that 10 rows of 9 tables would be 90 tables.

Student is unable to determine the number of students who can sit at 9 tables pushed together.

Student makes calculation errors that lead to an incorrect answer.

Student demonstrates some understanding of how to determine the number of students who can sit at 9 tables pushed together and some understanding of the need to divide 189 by 20 to see that it takes more than 9 rows.

What does a student at level 3 for standard F-BF.A.1a need to demonstrate in their explanation according to the rubric?

Student has errors in her table or graphs but provides a thorough written explanation that references the rates of change of the functions.

Student provides a limited written explanation but does not support the answer with tables or graphs.

Student provides a thorough written explanation that includes accurate references to the rates of change of the functions.

Student provides a table and/or a graph that may have minor errors but does not provide a correct explanation.

For standard F-IF.A.3, what is required for a student to achieve level 4 performance?

Student continues sequence correctly three times AND gives the correct number of dots.

Student does not demonstrate any understanding of the pattern of the sequence described in the problem.

Student has a significant error or omission in the task but demonstrates some understanding of the pattern of the sequence described in the problem.

Student has a minor error or omission in the task but demonstrates clear understanding of the pattern of the sequence described in the problem.

What does a student demonstrate if they correctly answer 2,550 and display sound reasoning in the explanation, using the pattern of the sequence to arrive at the answer?

C) Correct understanding of the pattern and sound reasoning.

A) No understanding of using the pattern to find the fifth term.

B) Only able to provide either the recursive or the explicit formula for a sequence.

D) Correct answer but with a calculation error and an explanation based on sound reasoning.

If a student is only able to provide either the recursive or the explicit formula for a sequence, but not both, and the formulas provided are incorrect, what level of understanding does the student demonstrate?

D) Some understanding but with incorrect formulas for both recursive and explicit cases.

A) No understanding of using the pattern to find the fifth term.

B) Correct understanding of the pattern and sound reasoning.

C) Correct answer but with a calculation error and an explanation based on sound reasoning.

When a student leaves the question blank or answers that it is not a function, what are they demonstrating in terms of understanding the function?

D) Lack of understanding in identifying the domain and range or the concept of a function.

A) No understanding of using the pattern to find the fifth term.

B) Correct understanding of the pattern and sound reasoning.

C) Some understanding but with incorrect formulas for both recursive and explicit cases.

According to the assessment criteria in section 4a, what indicates that a student does not have a sufficient understanding of what is required for a relation to be a function?

The student indicates the relation is not a function and provides no reasoning or incorrect reasoning.

The student provides a detailed explanation of the domain and range.

The student identifies the relation as a function but with minor errors.

The student correctly interprets the meaning of a given scenario.

In section 4b, what does it suggest if a student indicates a relation is a function but does not provide sufficient explanation or omits the naming of the domain and range?

The student has a partial understanding of what is required for a relation to be a function.

The student has a thorough understanding of functions.

The student is able to discern that the relation is not a function.

The student provides incorrect reasoning for why a relation is not a function.

What does section 5a suggest is a mistake a student might make when identifying the y-intercept of a function?

The student identifies the y-intercept as the point (0, 2350) but fails to relate it to the year 1950.

The student relates the y-intercept to the correct context of the problem.

The student provides a detailed explanation of the domain and range.

The student interprets the y-intercept as the population in the year 1950.

According to the assessment task, what is the correct interpretation when a student identifies that there are no intervals for which the function is increasing over its entire domain?

The student mathematically and correctly interprets the answer.

The student does not correctly interpret this answer in the context of the problem.

The student has minor errors or omissions in the language used to answer the questions.

The student makes a computational error in finding the slope.

When a student attempts to use the two data points to write a linear function but makes a significant error in arriving at the equation of the line, which parts of the assessment are likely incorrect?

Parts (f) and (g) are likely incorrect.

Parts (d) and (e) are likely incorrect.

Parts (a) and (b) are likely incorrect.

Only part (g) is likely incorrect.

What is the assessment of a student's understanding when they restrict the domain and explain the answer by considering that the domain should start in the year 1950 or considering that it does not make sense to continue the model when the population has fallen below zero, but does not consider both factors?

The student restricts the domain and explains the answer by either considering the year 1950 or considering that it does not make sense to continue the model when the population has fallen below zero but does not consider both factors.

The student does not demonstrate sound reasoning in restricting the domain.

The student makes an error in calculating the end points of the interval for the domain.

The student correctly calculates the end points of the interval for the domain.

Which of the following is a solution that evens out the rows and still uses as few tables as possible?

B) 5 rows of 6 tables and 10 rows of 5 tables

A) 8 rows of 9 tables, 1 row of 2 tables, and 6 rows of 1 table

C) 9 rows of 10 tables and 6 rows of 5 tables

Seating Arrangements Quiz Quiz

75 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many students can be seated around one table according to the diagram provided?

2 students

4 students

6 students

8 students

Tags

CCSS.3.MD.D.8

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When two tables are pushed together, how many students can sit around them?

4 students

6 students

8 students

10 students

Tags

CCSS.4.MD.A.2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of sequence is formed by the number of students who can sit at one table, two tables, and so on?

Arithmetic sequence

Geometric sequence

Neither arithmetic nor geometric sequence

Cannot be determined from the information provided

Tags

CCSS.HSF.BF.A.2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Using the pattern shown in the diagram, how many students can sit around 15 tables pushed together in a row?

30 students

32 students

34 students

36 students

Tags

CCSS.5.OA.B.3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If the cafeteria uses exactly 9 tables pushed together to make each row, how many rows will they need to seat 189 students?

A) 21 rows

B) 20 rows

C) 19 rows

D) 22 rows

Tags

CCSS.3.OA.A.3

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What will be the total number of tables used to seat all 189 students if 9 tables are pushed together to make each row?

A) 189 tables

B) 81 tables

C) 21 tables

D) 171 tables

Tags

CCSS.3.OA.A.3

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Is it possible to seat the 189 students with fewer total tables than when using 9 tables per row? If so, what is the fewest number of tables needed?

A) Yes, 20 tables

B) Yes, 18 tables

C) No, 9 tables per row is the minimum

D) Yes, 17 tables

Tags

CCSS.4.NBT.B.6

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Seating Arrangements Quiz

How many students can be seated around one table according to the diagram provided?

When two tables are pushed together, how many students can sit around them?

What type of sequence is formed by the number of students who can sit at one table, two tables, and so on?

Using the pattern shown in the diagram, how many students can sit around 15 tables pushed together in a row?

If the cafeteria uses exactly 9 tables pushed together to make each row, how many rows will they need to seat 189 students?

What will be the total number of tables used to seat all 189 students if 9 tables are pushed together to make each row?

Is it possible to seat the 189 students with fewer total tables than when using 9 tables per row? If so, what is the fewest number of tables needed?

How many tables would be used in each row if the fewest number of total tables is used to seat 189 students?

What is the function f(x) that Sydney was studying?

What is the function g(x) that Sydney was studying?

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